El Paso Chief of Police Gregory Allen told ABC News that violence "hasn't crossed into the town the way a lot of people might perceive.

"Not like it used to be," Allen said. "When I first came on the department, many of our crimes driven along the border and downtown resulted from illegal aliens in the country. That isn't the case as much now."

According to 2011 FBI figures, El Paso, population 660,000, has been America's safest big city for the past three years.

More surprising to those monitoring an immigration debate dominated by fear of crime imported from across the border is that six of the country's 10 safest cities are in high-immigration zones. San Diego is the second safest city, while Austin, Texas; San Jose, Calif.; Los Angeles and San Antonio, Texas, follow. New York City, Portland, Ore., Charlotte, N.C., and Seattle round out the safe-city list.

John Cook, who has been El Paso's mayor for eight years, took ABC News on a tour.

"For the most part, people who come into the United States don't want to get in trouble. They don't want to commit crimes," he said. "They just want to make a living. I call them economic refugees [because] they just came to try to secure the American dream and a better life for their families, not to commit crimes."

Cook said the combination of increased border patrol, a 131-mile fence that stretches from one end of El Paso -- Texas' sixth largest city -- out into the desert, and a better Mexican economy, have slowed undocumented immigration dramatically.

"I think there was a direct correlation between recession and the number of illegal apprehensions," Cook said.

When ABC News asked if an immigration overhaul should wait on a a secure border, Cook answered quickly: "We're ready to start right now because the border is secure."

"It's about as secure as you're ever going to get it," he said. "My part of the border is secure. ... The city's safe and secure. I think it's time for immigration reform."

Lifetime El Paso resident Pablo Lopez lives within sight of the Friendship Bridge between Juarez and El Paso. He remembers 20 years ago when the early morning sound of immigrant footsteps would regularly wake him as masses of the undocumented immigrants snuck into the United States to work.

"They were my alarm clock," he said.

Today, he said he rarely sees any undocumented immigrants slipping into the shadows from Juarez to work in the United States.

"Because of the hiring of border agents, the technology, the cameras," Lopez said, "it's not possible. Not that they can't, but you don't see it as much."

As far as safety goes, he said he lived in a low-income neighborhood, but the crime rate was low and the nights were quiet.

"We're all together trying to make our community safe," he said. "Here it's dead. When I get home at 7, I go out and there is nothing. It's a very safe, boring community. Quiet. It's calm."

Not everyone is convinced the drop in crime is connected to the plunging rate of undocumented immigration, even though the numbers are startling. In 1993, the border patrol apprehended 286,000 people crossing illegally into the United States and watched many more escape arrest. In 2012, 9,700 undocumented people were apprehended.